mathematics

Zdeněk Frolík

Zdeněk Frolík is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Zdeněk Frolík rather than just read about it. In short: Zdeněk Frolík (10 March 1933 – 3 May 1989) was a Czech mathematician. His research interests included topology and functional analysis.

Key takeaways

Zdeněk Frolík belongs to mathematics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Zdeněk Frolík to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Zdeněk Frolík from memory before moving on to harder problems.

Reference excerpt

Zdeněk Frolík (10 March 1933 – 3 May 1989) was a Czech mathematician. His research interests included topology and functional analysis. In particular, his work concerned covering properties of topological spaces, ultrafilters, homogeneity, measures, uniform spaces. He was one of the founders of modern descriptive theory of sets and spaces. Two classes of topological spaces are given Frolík's name: the class P of all spaces X {\displaystyle X} such that X × Y {\displaystyle X\times Y} is pseudocompact for every pseudocompact space Y {\displaystyle Y} , and the class C of all spaces X {\displaystyle X} such that X × Y {\displaystyle X\times Y} is countably compact for every countably compact space Y {\displaystyle Y} . Frolík prepared his Ph.D. thesis under the supervision of Miroslav Katetov and Eduard Čech.

Selected publications Generalizations of compact and Lindelöf spaces - Czechoslovak Math. J., 9 (1959), pp. 172–217 (in Russian, English summary) The topological product of countably compact spaces - Czechoslovak Math. J., 10 (1960), pp. 329–338 The topological product of two pseudocompact spaces - Czechoslovak Math. J., 10 (1960), pp. 339–349 Generalizations of the Gδ-property of complete metric spaces - Czechoslovak Math. J., 10 (1960), pp. 359–379 On the topological product of paracompact spaces - Bull. Acad. Polon., 8 (1960), pp. 747–750 Locally complete topological spaces - Dokl. Akad. Nauk SSSR, 137 (1961), pp. 790–792 (in Russian) Applications of complete families of continuous functions to the theory of Q-spaces - Czechoslovak Math. J., 11 (1961), pp. 115–133 Invariance of Gδ-spaces under mappings - Czechoslovak Math. J., 11 (1961), pp. 258–260 On almost real compact spaces - Bull. Acad. Polon., 9 (1961), pp. 247–250 On two problems of W.W. Comfort - Comment. Math. Univ. Carolin., 7 (1966), pp. 139–144 Non-homogeneity of βP- P - Comment. Math. Univ. Carolin., 7 (1966), pp. 705–710 Sums of ultrafilters - Bull. Amer. Math. Soc., 73 (1967), pp. 87–91 Homogeneity problems for extremally disconnected spaces - Comment. Math. Univ. Carolin., 8 (1967), pp. 757–763 Baire sets that are Borelian subspaces - Proc. Roy. Soc. A, 299 (1967), pp. 287–290 On the Suslin-graph theorem - Comment Math. Univ. Carolin., 9 (1968), pp. 243–249 A survey of separable descriptive theory of sets and spaces - Czechoslovak Math. J., 20 (1970), pp. 406–467 A measurable map with analytic domain and metrizable range is quotient - Bull. Amer. Math. Soc., 76 (1970), pp. 1112–1117 Luzin sets are additive - Comment Math. Univ. Carolin., 21 (1980), pp. 527–534 Refinements of perfect maps onto metrizable spaces and an application to Čech-analytic spaces - Topology Appl., 33 (1989), pp. 77–84 Decomposability of completely Suslin additive families - Proc. Amer. Math. Soc., 82 (1981), pp. 359–365 Applications of Luzinian separation principles (non-separable case) - Fund. Math., 117 (1983), pp. 165–185 Analytic and Luzin spaces (non-separable case) - Topology Appl., 19 (1985), pp. 129–156

Illustrations

Worked examples

Example 1 — a first encounter with Zdeněk Frolík

Start with the simplest possible case. Write down what Zdeněk Frolík claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Zdeněk Frolík before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Zdeněk Frolík ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Zdeněk Frolík

In research: Zdeněk Frolík appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Zdeněk Frolík in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Zdeněk Frolík is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1933 births, 1989 deaths, 20th-century Czech mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Zdeněk Frolík outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

Ask Teacher Smith questions about this articleOpens your AI tutor with a question about “Zdeněk Frolík” →

Affiliate

Preply — study more efficiently by working with a personal tutor. 50% off.

How to study Zdeněk Frolík in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Zdeněk Frolík means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Zdeněk Frolík out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Zdeněk Frolík in simple terms?

Zdeněk Frolík (10 March 1933 – 3 May 1989) was a Czech mathematician. His research interests included topology and functional analysis.

Why does Zdeněk Frolík matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Zdeněk Frolík?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Zdeněk Frolík.